A general descent framework for the monotone variational inequality problem

Hybrid steepest-descent method with sequential and functional errors in Banach space

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

Strong convergence of variational inequality problem Over the set of common fixed points of a family of demi-contractive mappings

In this paper, by using the viscosity iterative method and the hybrid steepest-descent method, we present a new algorithm for solving the variational inequality problem. The sequence generated by this algorithm is strong convergence to a common element of the set of common zero points of a finite family of inverse strongly monotone operators and the set of common fixed points of a finite family...

Modified Descent Methodsfor Solving the Monotonevariational

Recently, Fukushima proposed a diierentiable optimization framework for solving strictly monotone and continuously diierentiable variational inequalities. The main result of this paper is to show that Fukushima's results can be extended to monotone (not necessarily strictly monotone) and Lipschitz continuous (not necessarily continuously diierentiable) variational inequalities, if one is willin...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

A New Merit Function and an Sqp Method for Non-strictly Monotone Variational Inequalities

Merit functions utilized to monitor the convergence of sequential quadratic programming (SQP) methods for nonlinear programs and variational inequality problems have in common that they include a penalty function for the explicit constraints, the value of the penalty parameter for which is subject to the requirement of being large enough compared to estimates of the optimal Lagrange multipliers...